arXiv subjects

S. Cordero

Publications and source records attributed to S. Cordero.

15 recordsLinked to original sources

arXiv2026

Effect of the Atomic Dipole-Dipole Interaction on the Phase Diagrams of 2-Level Matter-Field Systems

Quantum information measures are used to study the quantum phase diagrams of a two-level extended Dicke model, including the particle dipole-dipole interaction, for a finite number of particles. This is treated both with and without the rotating-wave approximation. Differences are noted between these new diagrams and those obtained in the corresponding variational treatment. The standard deviation of the population inversion operator and the correlation of the number of parti- cles occupying the ground and excited levels, carry most of the information of the regions where a phase transition takes place. The correlation coefficient of the number of photons and the number of particles occupying the excited level yields information of the sudden changes in the behavior of the ground state of the composite system.

quant-ph↗

arXiv2024

Dynamic violation of Bell's inequalities in the angular momentum representation

A parametrization of density matrices of $d$ dimensions in terms of the raising $J_+$ and lowering $J_-$ angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A general expression for the density matrix of the composite system of angular momenta $j_1$ and $j_2$ is obtained. In this matrix representation violations of the Bell-Clauser-Horne-Shimony-Holt inequalities are established for the $X$-states of a qubit-qubit, pure and mixed, composite system, as well as for a qubit-qutrit density matrix. In both cases maximal violation of the Bell inequalities can be reached, i.e., the Cirel'son limit. A correlation between the entanglement measure and a strong violation of the Bell factor is also given. For the qubit-qutrit composite system a time-dependent convex combination of the density matrix of the eigenstates of a two-particle Hamiltonian system is used to determine periodic maximal violations of the Bell's inequality.

quant-ph↗

arXiv2024

Geometric properties of qudit systems

We discuss in general how to geometrically visualize a qudit system, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian systems with known average energy. These geometric characterizations are given in terms of the generalized diagonal Bloch vectors and the invariants of the special unitary group in $n$ dimensions. As examples, Hamiltonians written in terms of linear and quadratic generators of the angular momentum algebra are considered with $J= 1$ and $J=3/2$. For these cases, paths as functions of the temperature are established in the corresponding simplex representations, which show first- and second-order quantum phase transitions, as well as the adiabatic evolution of the interaction strengths (control parameters) of the Hamiltonian models. For the Lipkin-Meshkov-Glick Hamiltonian the quantum phase diagram is explicitly shown for different temperature values in parameter space.

quant-ph↗

arXiv2023

Storing Quantum Information in a generalised Dicke Model via a Simple Rotation

A method for storing quantum information is presented for $3$-level atomic systems interacting dipolarly with a single radiation field. The method involves performing simple local SU(2) rotations on the Hamiltonian. Under equal detuning, these transformations decouple one of the atomic levels from the electromagnetic field for the $\Lambda$- and $V$-configurations, yielding two effective $2$-level systems (qubits) plus an isolated atomic level; this allows for the exchange of information between the qubits. This rotation preserves the quantum phase diagram of the system. The method could possibly be used as a means to manipulate quantum information, such as storage and retrieval, or communication via a transmission line.

quant-ph↗

arXiv2023

Wigner Function Analysis of Finite Matter-Radiation Systems

We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum phase transitions take place. A finer classification for the continuous phase transitions is obtained through the computation of the surface of minimum fidelity.

quant-ph↗

arXiv2023

Geometry, quantum correlations, and phase transitions in the $\Lambda$-atomic configuration

The quantum phase diagram for a finite $3$-level system in the $\Lambda$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility and entanglement, applied to the reduced density matrix of the matter sector of the system. The quantum phases are explained by emphasizing the spontaneous symmetry breaking along the separatrix. Additionally, a description of the reduced density matrix of one atom in terms of a simplex allows a geometric representation of the entanglement and purity properties of the system. These concepts are calculated for both, the symmetry-adapted variational coherent states and the numerical diagonalisation of the Hamiltonian, and compared. The differences in purity and entanglement obtained in both calculations can be explained and visualised by means of this simplex representation.

quant-ph↗

arXiv2019

Optimal basis for the generalized Dicke model

A methodology is devised for building optimal bases for the generalized Dicke model based on the symmetry adapted variational solution to the problem. At order zero, the matter sector is constructed by distributing $N_a$ particles in all the possible two-level subsystems connected with electromagnetic radiation; the next order is obtained when the states of $N_a-1$ particles are added and distributed again into the two-level subsystems; and so on. In the electromagnetic sector, the order zero for each mode is the direct sum of the Fock spaces, truncated to a value of the corresponding constants of motion of each two-level subsystem; by including contributions of the other modes, the next orders are obtained. As an example of the procedure we consider $4$ atoms in the $Ξ$ configuration interacting dipolarly with two modes of electromagnetic radiation. The results may be applied to situations in quantum optics, quantum information, and quantum computing.

quant-ph↗

arXiv2017

Dynamic Generation of Light States with Discrete Symmetries

A dynamic procedure is established within the generalised Tavis-Cummings model to generate light states with discrete point symmetries, given by the cyclic group ${\cal C}_n$. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of $3$-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, $\vert ψ\rangle_{M_1}$, and $\vert ψ\rangle_{M_2}$, is considered. It can be generated by the proper selection of the time-of-flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order $n=\vert M_1-M_2\vert$.

quant-ph↗

arXiv2016

Variational Study of $λ$- and $N$-Atomic Configurations Interacting with an Electromagnetic Field of $2$ Modes

A study of the $λ$- and $N$-atomic configurations under dipolar interaction with $2$ modes of electromagnetic radiation is presented. The corresponding quantum phase diagrams are obtained by means of a variational procedure. Both configurations exhibit normal and collective (super-radiant) regimes. While the latter in the $λ$-configuration divides itself into $2$ subregions, corresponding to each of the modes, that in the $N$-configuration may be divided into $2$ or $3$ subregions depending on whether the field modes divide the atomic system into $2$ separate subsystems or not. Our variational procedure compares well with the exact quantum solution. The properties of the relevant field and matter observables are obtained.

quant-ph↗

arXiv2015

Symmetry Adapted Coherent States for Three-Level Atoms Interacting with One-Mode Radiation

We introduce a combination of coherent states as variational test functions for the atomic and radiation sectors to describe a system of Na three- level atoms interacting with a one-mode quantised electromagnetic field, with and without the rotating wave approximation, which preserves the symmetry presented by the Hamiltonian. These provide us with the possibility of finding analytical solutions for the ground and first excited states. We study the properties of these solutions for the V-configuration in the double resonance condition, and calculate the expectation values of the number of photons, the atomic populations, the total number of excitations, and their corresponding fluctuations. We also calculate the photon number distribution and the linear entropy of the reduced density matrix to estimate the entanglement between matter and radiation. For the first time, we exhibit analytical expressions for all of these quantities, as well as an analytical description for the phase diagram in parameter space, which distinguishes the normal and collective regions, and which gives us all the quantum phase transitions of the ground state from one region to the other as we vary the interaction parameters (the matter-field coupling constants) of the model, in functional form.

quant-ph↗

arXiv2015

Importance of pore length and geometry in the adsorption/desorption process: a molecular simulation study

Discrete potentials can describe properly the liquid vapor boundary that is necessary to model the adsorption of gas molecules in mesoporous systems with computer simulations. Although there are some works in this subject, the simulations are still highly time - consuming. Here we show that an efficient alternative is to use the three - dimensional Ising model, which allows one to model large systems, with geometries as complex as required that accurately represent the liquid vapor boundary. In particular, we report molecular simulations of cylindrical pores of two different geometry, using a discrete potential. The effect of the length of the pore in the hysteresis loop for a finite pore and infinite one is studied in detail. Lastly, we compare our predictions with experimental results and find excellent agreement between the area of the hysteresis loop predicted for the finite pore and that found in adsorption/desorption experiments.

cond-mat.soft↗

arXiv2015

Adsorption desorption processes on mesoscopic pores conected to microscopic pores of complex geometry using the Ising model

In this work we report studies of nitrogen adsorption and desorption onto solid surfaces using computer simulations of the three dimensional Ising model, for systems with complex porous structures at the mesoscopic and microscopic levels. A hysteresis cycle between the adsorption and desorption processes appears and we find that its characteristics are dependent on the geometry of the pore and on the strength of the surface fluid interaction. We obtained also an average adsorption isotherm, which represents a combination of differently shaped pores, and shows robust jumps at certain values of the chemical potential as a consequence of the structures of the pores. Lastly, we compare our results with experimental data and also report the filling process of microscopic pores connected with mesopores. It is argued that these predictions are useful for researchers working on the enhanced recovery of oil and for the design of new nanomaterials, among others.

cond-mat.soft↗

arXiv2014

Mirror symmetry in the energy spectra of $n$-level systems

The energy spectrum of a system of $N_a$ atoms of $n$ levels interacting with a one-mode electromagnetic field is studied in the dipole and rotating wave approximations. We find that, under the resonant condition, it exhibits a mirror symmetry with respect to the energy $E=M$ where $M$ the total number of excitations. Thus, for any eigenstate $|ψ_M^{+}\rangle$ with energy $E=M+{\cal E}$ there exists a related eigenstate $|ψ_M^{-}\rangle$ with energy $E=M-{\cal E}$ via the unitary parity operator in the number of photons . This is independent of the dipolar coupling between the levels. We give explicit examples for $3$-level systems.

quant-ph↗

arXiv2014

A triple point in 3-level systems

The energy spectrum of a 3-level atomic system in the $Ξ$-configuration is studied. This configuration presents a triple point independently of the number of atoms, which remains in the thermo- dynamic limit. This means that in a vicinity of this point any quantum fluctuation will drastically change the composition of the ground state of the system. We study the expectation values of the atomic population of each level, the number of photons, and the probability distribution of photons at the triple point.

quant-ph↗

arXiv2013

A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field

We consider $N_a$ three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the configurations $Ξ$, $Λ$ and $V$, with and without detuning. The semi-classical and exact quantum calculations for both the expectation values of the total number of excitations $\cal{M}=\langle \bm{M} \rangle$ and photon number $n=\langle \bm{n} \rangle$ have an excellent correspondence as functions of the control parameters. We prove that the ground state of the collective regime obeys sub-Poissonian statistics for the ${\cal M}$ and $n$ distribution functions. Therefore, their corresponding fluctuations are not well described by the semiclassical approximation. We show that this can be corrected by projecting the variational state to a definite value of ${\cal M}$.

quant-ph↗